Local hysteresis and grain size effect in Pb(Mg_1/3Nb _2/3)O₃-PbTiO₃ thin films

The local piezoelectric properties of relaxor ferroelectric films of solid solutions 0.9Pb(Mg_1/3Nb_2/3)O₃-0.1PbTiO ₃ were investigated by scanning force microscopy (SFM) in a piezoelectric contact mode. The piezoelectric hysteresis loops were acquired in the interior of grains of different sizes. A clear correlation between the values of the effective piezoelectric coefficients, d_eff, and the size of the respective grains is observed. Small grains exhibit slim piezoelectric hysteresis loops with low remanent d_eff, whereas relatively strong piezoelectric activity is characteristic of larger grains. Part of the grains (∼20-25%) is strongly polarized without application of a dc field. The nature of both phenomena is discussed in terms of the internal bias field and grain size effects on the dynamics of nanopolar clusters.